Please answer problems $1,2,$ and $3.$

Problem $1$:

The rope CE exerts an $850$ N force $T$ on the hinged door.

Determine the unit vector of $T$;

Determine the vector component of $T,\frac{T}{\frac{?}{?}}$ parallel to the line CA ;

Determine the vector component of $|{)}_{?}$ perpendicular to the line $CA.$

$****($Optional$)$

Determine the shortest distance from E to the line CA $.$

Problem $2$:

Suppose that the cross product of two vectors $U$ and $V$ is $UV=0.$ If $U0,$ what do you know

about the vector $V?$

Problem $3$:

Two vectors are given in terms of their components by $r=2i-3j+4k$ and $F=20i-10k.$

Determine the cross$-$product $rF$;

Determine the cross$-$product $Fr$;

Calculate the components of the unit vector that is perpendicular to the plane defined by $r$

and $F.$